# The force applied against a moving object travelling on a linear path is given by F(x)=3xe^x . How much work would it take to move the object over x in [2, 7] ?

##### 1 Answer
Nov 12, 2016

I got: $W = 19 , 717 J$

#### Explanation:

Here you have a variable force (changes with distance $x$) so to evaluate the Work we need to use the integral version as:

$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx}$

or, in your case:

$W = {\int}_{2}^{7} \left(3 x {e}^{x}\right) \mathrm{dx} =$ by parts:

$= 3 \left[x {e}^{x} - {e}^{x}\right]$ between $x = 2$ and $x = 7$ gives you:

$W = 19 , 717 J$